1. Algebra 1
Section 13.7

2. Motion Problems
The basic equation used here is r • t = d.

3. Example 1
r • t = d
Upstream
Downstream d d
The variable here is d, the distance traveled up and down the river.

4. Example 1
r • t = d
Upstream
Downstream 2 d 8 d
The upstream rate is 5 – 3 = 2; the downstream rate is = 8 (mi/hr).

5. Example 1
r • t = d
Upstream
Downstream 2
d/2 d 8
d/8 d
Time is calculated by dividing the distance by the rate.

6. Example 1 r • t = d 2 d/2 d 8 d/8 d d 2 8 + = 5
Upstream
Downstream 2
d/2 d 8
d/8 d d 2 8
= 5
Using the times given in the problem, we observe they spent 5 hours paddling.

7. Example 1 d 2 8
= 5 8
( )8
4d + d = 40
5d = 40
d = 8

8. Example 1 d = 8 The distance up the river is 8 miles.
Upstream time is d/2 = 4 hr.
They stopped for lunch at 1:00 PM.
Downstream time is d/8 = 1 hr.

9. Example 2 r • t = d r 6r Let r = the speed of the car
By car
By plane r 6r
Let r = the speed of the car
6r = the speed of the plane

10. Example 2
r • t = d
By car
By plane r
780 6r
780
In both cases, the distance is 780 miles.

11. Example 2
r • t = d
By car
By plane r
780/r
780 6r
780/6r
780
Time is calculated by dividing the distance by the rate.

12. Example 2
r • t = d
By car
By plane r
780/r
780 6r
780/6r
780
It is helpful to think of 12½ as 25/2 when writing the equation.
780 r 6r = 25 2

13. Example 2 780 r 6r = + 25 2 The LCD is 6r. 780 r 6r= 25 2
The LCD is 6r.
780 r 6r
6r ( ) = 6r ( ) + 6r ( ) 25 2
4680 =
780 +
75r

14. Example 2 4680 = 780 + 75r 3900 = 75r r = 52 mi/hr 6r = 312 mi/hr
The time for the car is 15 hr.
The time for the plane is 2½ hr.

15. Work Problems
The amount of work done in one hour is the reciprocal of the number of hours worked.
If a job takes 4 hours, then ¼ can be completed in one hour.

16. Example 3
Let m = the number of minutes it should take them to do the job together.
Allison can do 1 chapter per 60 minutes.
Sean can do 1 chapter per 75 minutes.

17. Example 3 1 60 75 + = 1 m The LCD is 300m. 5m + 4m = 300 9m = 300= 1 m
The LCD is 300m.
5m +
4m =
300
9m = 300
100 3
m = = 33⅓ min

18. Example 3 Always check to see that your solution is reasonable.
Notice that the answer is not the average of half of each person’s times.

19. Example 4
Let h = the number of hours it should take for Ned to do the job.
Mr. Mathews can do 1 job per 10 hours.
Together, they can do 1 job per 4 hours.

20. Example 4 1 10 h + = 1 4 The LCD is 20h. 2h + 20 = 5h 20 = 3h= 1 4
The LCD is 20h.
2h +
20 = 5h
20 = 3h 20 3
h = = 6⅔ hr

21. Homework: pp